There's a few ways the president can impact the economy, though not by themself. Usually the majority of the rest of the government is involved too.

The first is that the president is de facto leader of their party. This isn't an enumerated power, but traditionally the way the parties work. So the president, usually, has a lot of cooperation from their party's Congressional members.

Second, it is generally typical for the House and Senate to switch to the control of the same party as the president. This is due to general voting attitudes, as most people vote down the ticket for their party. This can vary with Congressional term limits though.

Third, veto power. Even when Congress and the President are not aligned, the president can veto laws that would have a significant impact on the economy. The opposition party would need a super majority to override that veto.

Lastly, there is executive order. This can impact foreign trade, infrastructure, and regulations. Sometimes these are found unlawful by the courts and rescinded, but they can still have had an impact before then.